Tournament solutions are standard tools for identifying winners based on pairwise comparisons between competing alternatives. The recently studied notion of margin of victory (MoV) offers a general method for refining the winner set of any given tournament solution, thereby increasing the discriminative power of the solution. In this paper, we reveal a number of structural insights on the MoV by investigating fundamental properties such as monotonicity and consistency with respect to the covering relation. Furthermore, we provide experimental evidence on the extent to which the MoV notion refines winner sets in tournaments generated according to various stochastic models.

翻译：锦标赛解法是基于竞争方案间两两比较确定获胜者的标准工具。近期提出的获胜优势（MoV）概念为任意锦标赛解法的获胜者集合提供了一般性精炼方法，从而提升了解法的区分能力。本文通过研究单调性、覆盖关系一致性等基本性质，揭示了获胜优势的结构性洞见。此外，我们提供了实验证据，证明获胜优势概念在根据多种随机模型生成的锦标赛中对获胜者集合的精炼程度。